diff --git a/lib/msun/src/s_cospi.c b/lib/msun/src/s_cospi.c index 92a5f467c97f..860219efd3e4 100644 --- a/lib/msun/src/s_cospi.c +++ b/lib/msun/src/s_cospi.c @@ -1,151 +1,152 @@ /*- * Copyright (c) 2017 Steven G. Kargl * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice unmodified, this list of conditions, and the following * disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /** * cospi(x) computes cos(pi*x) without multiplication by pi (almost). First, * note that cospi(-x) = cospi(x), so the algorithm considers only |x|. The * method used depends on the magnitude of x. * * 1. For small |x|, cospi(x) = 1 with FE_INEXACT raised where a sloppy * threshold is used. The threshold is |x| < 0x1pN with N = -(P/2+M). * P is the precision of the floating-point type and M = 2 to 4. * * 2. For |x| < 1, argument reduction is not required and sinpi(x) is * computed by calling a kernel that leverages the kernels for sin(x) * ans cos(x). See k_sinpi.c and k_cospi.c for details. * * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where * |x| = j0 + r with j0 an integer and the remainder r satisfies * 0 <= r < 1. With the given domain, a simplified inline floor(x) * is used. Also, note the following identity * * cospi(x) = cos(pi*(j0+r)) * = cos(pi*j0) * cos(pi*r) - sin(pi*j0) * sin(pi*r) * = cos(pi*j0) * cos(pi*r) * = +-cospi(r) * * If j0 is even, then cos(pi*j0) = 1. If j0 is odd, then cos(pi*j0) = -1. * cospi(r) is then computed via an appropriate kernel. * * 4. For |x| >= 0x1p(P-1), |x| is integral and cospi(x) = 1. * * 5. Special cases: * * cospi(+-0) = 1. * cospi(n.5) = 0 for n an integer. * cospi(+-inf) = nan. Raises the "invalid" floating-point exception. * cospi(nan) = nan. Raises the "invalid" floating-point exception. */ +#include #include "math.h" #include "math_private.h" static const double pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */ pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */ #include "k_cospi.h" #include "k_sinpi.h" volatile static const double vzero = 0; double cospi(double x) { double ax, c; uint32_t hx, ix, j0, lx; EXTRACT_WORDS(hx, lx, x); ix = hx & 0x7fffffff; INSERT_WORDS(ax, ix, lx); if (ix < 0x3ff00000) { /* |x| < 1 */ if (ix < 0x3fd00000) { /* |x| < 0.25 */ if (ix < 0x3e200000) { /* |x| < 0x1p-29 */ if ((int)ax == 0) return (1); } return (__kernel_cospi(ax)); } if (ix < 0x3fe00000) /* |x| < 0.5 */ c = __kernel_sinpi(0.5 - ax); else if (ix < 0x3fe80000){ /* |x| < 0.75 */ if (ax == 0.5) return (0); c = -__kernel_sinpi(ax - 0.5); } else c = -__kernel_cospi(1 - ax); return (c); } if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */ /* Determine integer part of ax. */ j0 = ((ix >> 20) & 0x7ff) - 0x3ff; if (j0 < 20) { ix &= ~(0x000fffff >> j0); lx = 0; } else { lx &= ~((uint32_t)0xffffffff >> (j0 - 20)); } INSERT_WORDS(x, ix, lx); ax -= x; EXTRACT_WORDS(ix, lx, ax); if (ix < 0x3fe00000) { /* |x| < 0.5 */ if (ix < 0x3fd00000) /* |x| < 0.25 */ c = ix == 0 ? 1 : __kernel_cospi(ax); else c = __kernel_sinpi(0.5 - ax); } else { if (ix < 0x3fe80000) { /* |x| < 0.75 */ if (ax == 0.5) return (0); c = -__kernel_sinpi(ax - 0.5); } else c = -__kernel_cospi(1 - ax); } if (j0 > 30) x -= 0x1p30; j0 = (uint32_t)x; return (j0 & 1 ? -c : c); } if (ix >= 0x7f800000) return (vzero / vzero); /* * |x| >= 0x1p52 is always an even integer, so return 1. */ return (1); } #if LDBL_MANT_DIG == 53 __weak_reference(cospi, cospil); #endif diff --git a/lib/msun/src/s_sinpi.c b/lib/msun/src/s_sinpi.c index b9731112a7eb..858459a5fcb4 100644 --- a/lib/msun/src/s_sinpi.c +++ b/lib/msun/src/s_sinpi.c @@ -1,168 +1,169 @@ /*- * Copyright (c) 2017 Steven G. Kargl * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice unmodified, this list of conditions, and the following * disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /** * sinpi(x) computes sin(pi*x) without multiplication by pi (almost). First, * note that sinpi(-x) = -sinpi(x), so the algorithm considers only |x| and * includes reflection symmetry by considering the sign of x on output. The * method used depends on the magnitude of x. * * 1. For small |x|, sinpi(x) = pi * x where a sloppy threshold is used. The * threshold is |x| < 0x1pN with N = -(P/2+M). P is the precision of the * floating-point type and M = 2 to 4. To achieve high accuracy, pi is * decomposed into high and low parts with the high part containing a * number of trailing zero bits. x is also split into high and low parts. * * 2. For |x| < 1, argument reduction is not required and sinpi(x) is * computed by calling a kernel that leverages the kernels for sin(x) * ans cos(x). See k_sinpi.c and k_cospi.c for details. * * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where * |x| = j0 + r with j0 an integer and the remainder r satisfies * 0 <= r < 1. With the given domain, a simplified inline floor(x) * is used. Also, note the following identity * * sinpi(x) = sin(pi*(j0+r)) * = sin(pi*j0) * cos(pi*r) + cos(pi*j0) * sin(pi*r) * = cos(pi*j0) * sin(pi*r) * = +-sinpi(r) * * If j0 is even, then cos(pi*j0) = 1. If j0 is odd, then cos(pi*j0) = -1. * sinpi(r) is then computed via an appropriate kernel. * * 4. For |x| >= 0x1p(P-1), |x| is integral and sinpi(x) = copysign(0,x). * * 5. Special cases: * * sinpi(+-0) = +-0 * sinpi(+-n) = +-0, for positive integers n. * sinpi(+-inf) = nan. Raises the "invalid" floating-point exception. * sinpi(nan) = nan. Raises the "invalid" floating-point exception. */ +#include #include "math.h" #include "math_private.h" static const double pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */ pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */ #include "k_cospi.h" #include "k_sinpi.h" volatile static const double vzero = 0; double sinpi(double x) { double ax, hi, lo, s; uint32_t hx, ix, j0, lx; EXTRACT_WORDS(hx, lx, x); ix = hx & 0x7fffffff; INSERT_WORDS(ax, ix, lx); if (ix < 0x3ff00000) { /* |x| < 1 */ if (ix < 0x3fd00000) { /* |x| < 0.25 */ if (ix < 0x3e200000) { /* |x| < 0x1p-29 */ if (x == 0) return (x); /* * To avoid issues with subnormal values, * scale the computation and rescale on * return. */ INSERT_WORDS(hi, hx, 0); hi *= 0x1p53; lo = x * 0x1p53 - hi; s = (pi_lo + pi_hi) * lo + pi_lo * hi + pi_hi * hi; return (s * 0x1p-53); } s = __kernel_sinpi(ax); return ((hx & 0x80000000) ? -s : s); } if (ix < 0x3fe00000) /* |x| < 0.5 */ s = __kernel_cospi(0.5 - ax); else if (ix < 0x3fe80000) /* |x| < 0.75 */ s = __kernel_cospi(ax - 0.5); else s = __kernel_sinpi(1 - ax); return ((hx & 0x80000000) ? -s : s); } if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */ /* Determine integer part of ax. */ j0 = ((ix >> 20) & 0x7ff) - 0x3ff; if (j0 < 20) { ix &= ~(0x000fffff >> j0); lx = 0; } else { lx &= ~((uint32_t)0xffffffff >> (j0 - 20)); } INSERT_WORDS(x, ix, lx); ax -= x; EXTRACT_WORDS(ix, lx, ax); if (ix == 0) s = 0; else { if (ix < 0x3fe00000) { /* |x| < 0.5 */ if (ix < 0x3fd00000) /* |x| < 0.25 */ s = __kernel_sinpi(ax); else s = __kernel_cospi(0.5 - ax); } else { if (ix < 0x3fe80000) /* |x| < 0.75 */ s = __kernel_cospi(ax - 0.5); else s = __kernel_sinpi(1 - ax); } if (j0 > 30) x -= 0x1p30; j0 = (uint32_t)x; if (j0 & 1) s = -s; } return ((hx & 0x80000000) ? -s : s); } if (ix >= 0x7f800000) return (vzero / vzero); /* * |x| >= 0x1p52 is always an integer, so return +-0. */ return (copysign(0, x)); } #if LDBL_MANT_DIG == 53 __weak_reference(sinpi, sinpil); #endif diff --git a/lib/msun/src/s_tanpi.c b/lib/msun/src/s_tanpi.c index e01917c94c15..01d4c74367fd 100644 --- a/lib/msun/src/s_tanpi.c +++ b/lib/msun/src/s_tanpi.c @@ -1,176 +1,177 @@ /*- * Copyright (c) 2017 Steven G. Kargl * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice unmodified, this list of conditions, and the following * disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /** * tanpi(x) computes tan(pi*x) without multiplication by pi (almost). First, * note that tanpi(-x) = -tanpi(x), so the algorithm considers only |x| and * includes reflection symmetry by considering the sign of x on output. The * method used depends on the magnitude of x. * * 1. For small |x|, tanpi(x) = pi * x where a sloppy threshold is used. The * threshold is |x| < 0x1pN with N = -(P/2+M). P is the precision of the * floating-point type and M = 2 to 4. To achieve high accuracy, pi is * decomposed into high and low parts with the high part containing a * number of trailing zero bits. x is also split into high and low parts. * * 2. For |x| < 1, argument reduction is not required and tanpi(x) is * computed by a direct call to a kernel, which uses the kernel for * tan(x). See below. * * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where * |x| = j0 + r with j0 an integer and the remainder r satisfies * 0 <= r < 1. With the given domain, a simplified inline floor(x) * is used. Also, note the following identity * * tan(pi*j0) + tan(pi*r) * tanpi(x) = tan(pi*(j0+r)) = ---------------------------- = tanpi(r) * 1 - tan(pi*j0) * tan(pi*r) * * So, after argument reduction, the kernel is again invoked. * * 4. For |x| >= 0x1p(P-1), |x| is integral and tanpi(x) = copysign(0,x). * * 5. Special cases: * * tanpi(+-0) = +-0 * tanpi(+-n) = +-0, for positive integers n. * tanpi(+-n+1/4) = +-1, for positive integers n. * tanpi(+-n+1/2) = NaN, for positive integers n. * tanpi(+-inf) = NaN. Raises the "invalid" floating-point exception. * tanpi(nan) = NaN. Raises the "invalid" floating-point exception. */ +#include #include "math.h" #include "math_private.h" static const double pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */ pi_lo = -2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */ /* * The kernel for tanpi(x) multiplies x by an 80-bit approximation of * pi, where the hi and lo parts are used with with kernel for tan(x). */ static inline double __kernel_tanpi(double x) { double_t hi, lo, t; if (x < 0.25) { hi = (float)x; lo = x - hi; lo = lo * (pi_lo + pi_hi) + hi * pi_lo; hi *= pi_hi; _2sumF(hi, lo); t = __kernel_tan(hi, lo, 1); } else if (x > 0.25) { x = 0.5 - x; hi = (float)x; lo = x - hi; lo = lo * (pi_lo + pi_hi) + hi * pi_lo; hi *= pi_hi; _2sumF(hi, lo); t = - __kernel_tan(hi, lo, -1); } else t = 1; return (t); } volatile static const double vzero = 0; double tanpi(double x) { double ax, hi, lo, t; uint32_t hx, ix, j0, lx; EXTRACT_WORDS(hx, lx, x); ix = hx & 0x7fffffff; INSERT_WORDS(ax, ix, lx); if (ix < 0x3ff00000) { /* |x| < 1 */ if (ix < 0x3fe00000) { /* |x| < 0.5 */ if (ix < 0x3e200000) { /* |x| < 0x1p-29 */ if (x == 0) return (x); /* * To avoid issues with subnormal values, * scale the computation and rescale on * return. */ INSERT_WORDS(hi, hx, 0); hi *= 0x1p53; lo = x * 0x1p53 - hi; t = (pi_lo + pi_hi) * lo + pi_lo * hi + pi_hi * hi; return (t * 0x1p-53); } t = __kernel_tanpi(ax); } else if (ax == 0.5) return ((ax - ax) / (ax - ax)); else t = - __kernel_tanpi(1 - ax); return ((hx & 0x80000000) ? -t : t); } if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */ /* Determine integer part of ax. */ j0 = ((ix >> 20) & 0x7ff) - 0x3ff; if (j0 < 20) { ix &= ~(0x000fffff >> j0); lx = 0; } else { lx &= ~(((uint32_t)(0xffffffff)) >> (j0 - 20)); } INSERT_WORDS(x,ix,lx); ax -= x; EXTRACT_WORDS(ix, lx, ax); if (ix < 0x3fe00000) /* |x| < 0.5 */ t = ax == 0 ? 0 : __kernel_tanpi(ax); else if (ax == 0.5) return ((ax - ax) / (ax - ax)); else t = - __kernel_tanpi(1 - ax); return ((hx & 0x80000000) ? -t : t); } /* x = +-inf or nan. */ if (ix >= 0x7f800000) return (vzero / vzero); /* * |x| >= 0x1p52 is always an integer, so return +-0. */ return (copysign(0, x)); } #if LDBL_MANT_DIG == 53 __weak_reference(tanpi, tanpil); #endif